If the side of square is increased by 6%, then what will be the percentage increase in its area?

Options

A. 13.2
B. 12.04
C. 12.12
D. 12.36

Answer

To solve the problem of finding the percentage increase in the area of a square when its side is increased by 6%, we can follow these steps:

### Step 1: Understand the initial area of the square
Let the initial side length of the square be \( s \). The area \( A \) of the square is given by the formula:
\[ A = s^2 \]

### Step 2: Calculate the new side length after the increase
If the side length is increased by 6%, the new side length \( s' \) can be calculated as:
\[ s' = s + 0.06s = 1.06s \]

### Step 3: Calculate the new area of the square
The area of the square with the new side length \( s' \) is:
\[ A' = (s')^2 = (1.06s)^2 = 1.1236s^2 \]

### Step 4: Calculate the increase in area
The increase in area \( \Delta A \) is given by:
\[ \Delta A = A' - A = 1.1236s^2 - s^2 = (1.1236 - 1)s^2 = 0.1236s^2 \]

### Step 5: Calculate the percentage increase in area
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A} \right) \times 100 = \left( \frac{0.1236s^2}{s^2} \right) \times 100 = 12.36\% \]

### Conclusion
The percentage increase in the area of the square when the side is increased by 6% is **12.36%**.

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